Seems to me that I read, somewhere, that one has to be
really careful when using i. Specifically, I think that the problem, here, is that i is being defined as sqr(-1), which is not quite true; i^2 = -1 (since afaik, i was created as being the solution to the equation: x^2 + 1 = 0), but this would mean that, really, i =
+/- sqr(-1), while "sqr(-1)" just means "the principal, or positive, square root of -1" (I am, of course, substituting my clumsy typography "sqr()" for the symbol that you have used).
Anyway, the consequence of limiting the definition of i, to sqr(-1), only, appears with:
if you simplify the fraction on the right, in the second equation, by multiplying its numerator and denominator by i, you get:
i/1 = i/(i^2)
which then would simplify to:
i/1 = i/(-1)
i = -i
And then, this flaw is carried through with further operations, eventually resulting in:
So, I guess that's the problem, here: invalid assumption that sqr(-1) is equivalent to i.
(I can't believe that
I'm actually solving math puzzles)